M.Yamakita

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Intelligent Control, Its evolution, Recent
Technology on Robotics

• M.Yamakita
• Dept. of Mechanical and Control Systems Eng.
• Tokyo Inst. Of Tech.

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Key Technology of Intelligent Control
1. Machine Learning
(Iterative Learning Control Q-Learning
) 2. Physically Inspired Non-Linear Control
( Passivity Based (Adaptive ) Control) 3.
Fuzzy Control Stability Issue 4. Evolutional
Algorithm 5. Hybrid System
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Hierarchical Intelligent Control
PRECISION
INTELLIGENCE
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Execution Level
Coordination Level
(PID etc.)
Iterative Learning Control (ILC)
y(t)
r(t)
P
C
If the same operation is repeated, can we reduce
the error based on the error of the
previous trial ?
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Structure of ILC
Plant
Learning Filter
Memory
-

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Q-Learning
Statistic Iterative Optimization Method
Learning of optimal sequence of actions
Q table
a1 a2 a3
S1 Q(1,1) Q(1,1) Q(1,1)
S2 Q(1,1) Q(1,1) Q(1,1)
S3 Q(1,1) Q(1,1) Q(1,1)
S4 Q(1,1) Q(1,1) Q(1,1)
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Learning Rule
Action Section
Randomly select action j at state i by a
probability
(T is artificial temperature)
Update of Q-Table
aj
r(si,aj) is positive reward
Si
S
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New Representation of Systems
State Space Represenation
Port-Controlled Hamiltonian System Representation
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Shift of Equilibrium State
Disturbance Attenuation
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Control Example
Mechanical Equation
Generator Electrical Dynamics
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Evolutional Computation (EC)
Optimization Method inspired by Gene Dynamics
Example Travel Salesman Problem
Coding

1 2 3 4 5
A ?
B ?
C ?
D ?
E ?
. .
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Evolutional Operations (I)
Selection and Duplication
n
g1
g2
gn
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Evolutional Operations (II)
Permutation
Optimization Process
START
Coding
Evolutional Operation
Mutation
Good Gen ?
END
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Stability Issue of Fuzzy Control
Takagi-Sugeno Model
If x is M11 and x is M12 then
. .
If x is Mn1 and x is Mn2 then
Singleton Fuzzifier Product Inference
Weighted Average Deffuzifier
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Sufficient Condition of Stability of TS Model
Theorem If there exists a positive definite
matrix P satisfying
then the TS mode is globally asymptotically
stable.
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Proof of the Theorem
Let consider a following criterion function as a
candidate of Lyapunov function
Time derivative of the function along the
trajectory is given by
From the Lyapunov stability theorem, we have the
conclusion.
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Hybrid System
Roughly Speaking
Hybrid System Automation Differential/Differen
ce Eq.
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Formal Definition of a Hybrid System
Controller (Discrete Event SystemDES)
Plant
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Generation of Event
State transition of controller is occurred
immediately when
is generated.
Detection of event
Generation of event
Generation of input
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Simple Example (Temperature Control)
35
30
off
on
V
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References

• Watkins eta. Technical Note Q-Learning,
  Machine Learning 8, pp. 279/292 (1992)
• M.Yamakita and K.Furuta
• T.Shen eta. Adaptive L2 Disturbance Attenuation
  of Hamiltonian Systems with Parametric
  Perturbation and Application to Power Systems,
  submitted to Asian Journal of Control (2000)
• D.B.Fogel Evolutionary Computation A New
  Transactions, IEEE Trans. On Evolutionary
  Computation, 1-1, 1(1998)
• S.S.Farinwata eta. Ed.Fuzzy Control, Wiley
  (2000)
• K.Hirota eta. Soft-Computing as a Breakthrough,
  Vol.39, Mach 2000, J. of SICE (2000) (in
  Japanese)